Question

Consider the following hypothesis test. H0: p ≥ 0.75 Ha: p < 0.75 A sample of 280 items was selected. Compute the p-value and state your conclusion for each of the following sample results. Use α = 0.05. (a) p = 0.67 Find the value of the test statistic. (Round your answer to two decimal places.) Find the p-value. (Round your answer to four decimal places.) p-value = State your conclusion. Do not reject H0. There is sufficient evidence to conclude that p < 0.75. Reject H0. There is sufficient evidence to conclude that p < 0.75. Reject H0. There is insufficient evidence to conclude that p < 0.75. Do not reject H0. There is insufficient evidence to conclude that p < 0.75. (b) p = 0.72 Find the value of the test statistic. (Round your answer to two decimal places.) Find the p-value. (Round your answer to four decimal places.) p-value = State your conclusion. Do not reject H0. There is sufficient evidence to conclude that p < 0.75. Reject H0. There is sufficient evidence to conclude that p < 0.75. Reject H0. There is insufficient evidence to conclude that p < 0.75. Do not reject H0. There is insufficient evidence to conclude that p < 0.75. (c) p = 0.70 Find the value of the test statistic. (Round your answer to two decimal places.) Find the p-value. (Round your answer to four decimal places.) p-value = State your conclusion. Do not reject H0. There is sufficient evidence to conclude that p < 0.75. Reject H0. There is sufficient evidence to conclude that p < 0.75. Reject H0. There is insufficient evidence to conclude that p < 0.75. Do not reject H0. There is insufficient evidence to conclude that p < 0.75. (d) p = 0.77 Find the value of the test statistic. (Round your answer to two decimal places.) Find the p-value. (Round your answer to four decimal places.) p-value = State your conclusion. Do not reject H0. There is sufficient evidence to conclude that p < 0.75. Reject H0. There is sufficient evidence to conclude that p < 0.75. Reject H0. There is insufficient evidence to conclude that p < 0.75. Do not reject H0. There is insufficient evidence to conclude that p < 0.75.

Answer 1

Hypothesis : VS

Since , n=280

a) For p=0.67

The test statistic is ,

P-value =

Decision : Here , P-value = 0.0010 < 0.05

Therefore , reject Ho .

Conclusion : There is sufficient evidence to conclude that p < 0.75.

b) For p=0.72

The test statistic is ,

P-value =

Decision : Here , P-value = 0.1251 >  0.05

Therefore , Do not reject Ho .

Conclusion : There is insufficient evidence to conclude that p < 0.75.

c) For p=0.70

The test statistic is ,

P-value =

Decision : Here , P-value = 0.0274 < 0.05

Therefore , reject Ho .

Conclusion : There is sufficient evidence to conclude that p < 0.75.

d) For p=0.77

The test statistic is ,

P-value =

Decision : Here , P-value = 0.2206 > 0.05

Therefore , Do not reject Ho .

Conclusion : There is insufficient evidence to conclude that p < 0.75.